5.6 Rules of Exponents and Scientific Notation 273 In Exercises 49–56, (a) perform the indicated operation without the use of a calculator and express each answer in scientific notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in decimal notation, convert the answer to scientific notation. 49. (200,000)(3600) × 7.2 108 50. (230,000)(3000) × 6.9 108 51. (0.003)(0.00015) × − 4.5 10 7 52. (50,000)(0.00011) × 5.5 100 53. 5,600,000 80,000 × 7.0 101 54. 28,000 0.004 × 7.0 106 55. 0.00004 200 × − 2.0 10 7 56. 0.0012 0.000006 × 2.0 102 Problem Solving In Exercises 57– 60, list the numbers from smallest to largest. 57. × × × − 1.03 10 ; 1.7; 3.6 10 ; 9.8 10 4 3 2 × × × − 3.6 10 ; 1.7; 9.8 10 ; 1.03 10 3 2 4 58. × × × × − − 8.5 10 ; 8.2 10 ; 1.3 10 ; 6.2 10 5 3 1 4 × × × × − − 8.5 10 ; 1.3 10 ; 8.2 10 ; 6.2 10 5 1 3 4 59. × × − 40,000; 4.1 10 ; 0.00079; 8.3 10 3 5 × × − 8.3 10 ; 0.00079; 4.1 10 ; 40,000 5 3 60. × × 267,000,000; 3.14 10 ; 1,962,000; 4.79 10 7 6 × × 1,962,000; 4.79 10 ; 3.14 10 ; 267,000,000 6 7 In Exercises 61–78, use a scientific calculator to perform the necessary operations. 61. U.S. Debt per Person in 2018 Versus 2023 In Example 12, it was found that the U.S. national debt in 2023 was about $95,281.90 per person. In 2018, the U.S. national debt was about $21.97 trillion, and the U.S. population was about 323 million people. a) Determine the amount of debt per person in 2018. $68,018.58 b) How much more per person did the U.S. government owe in 2023 than in 2018? $27,263.32 62. Italy’s Debt per Person In 2023, the Italian national debt was about 2.81 trillion euros (the euro is the unit of currency in Italy). Italy’s population in 2023 was about 58.96 million people. a) Determine the amount of debt per person in Italy in 2023. 47,659.43 euros b) On June 24, 2023, 1 euro was worth about $1.09. Convert the amount determined in part (a) to dollars $51,948.78 63. U.S. Population On June 24, 2023, the population of the United States was about 337 million people, and the population of the world was about 8.04 billion people. Determine the ratio of the U.S. population to the world’s population by dividing the U.S. population by the world’s population. Write your answer as a decimal number to the nearest thousandth. 0.042 64. China’s Population. On June 24, 2023, the population of China was about 1.43 billion people, and the population of the world was about 8.04 billion people. Determine the ratio of China’s population to the world’s population by dividing China’s population by the world’s population. Write your answer as a decimal number to the nearest thousandth. 0.178 65. Gross Domestic Product The gross domestic product (GDP) of a country is the total output of goods and services produced within that country. In 2023, the GDP of the United States was about $26.24 trillion, and the U.S. population was about 337 million people. Determine the U.S. GDP per person by dividing the GDP by the population. $77,863.50 66. China’s GDP In 2023, the GDP (see Exercise 65) of China was about $19.37 trillion, and the population of China was about 1.43 billion people. Determine China’s GDP per person by dividing the GDP by the population. $13,545.45 67. Traveling to the Moon The distance from Earth to the moon is approximately 239,000 mi. If a spacecraft travels at a speed of 20,000 mph, how many hours would the spacecraft need to travel from Earth to the moon? Use = × distance rate time. 11.95 hours 68. Traveling to Proxima Centauri The star closest in distance to our own sun is Proxima Centauri. The distance from Earth to Proxima Centauri is approximately × 2.5 10 miles. 13 If a spacecraft travels at a speed of 20,000 mph, how many hours would the spacecraft need to travel to Proxima Centauri? Use = × distance rate time and write your answer in scientific notation. × 1.25 10 hours 9 69. 1950 Niagara Treaty The 1950 Niagara Treaty between the United States and Canada requires that during the tourist season a minimum of 100,000 cubic feet of water per second (ft /sec) 3 flow over Niagara Falls (another − 130,000 160,000 ft /sec 3 are diverted for power generation). Determine the minimum amount of water that will flow over the falls in a 24-hour period during the tourist season. Write your answer in scientific notation. × 8.64 10 ft 9 3 Pjmorley/Shutterstock
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